Informatics and Applications
2022, Volume 16, Issue 1, pp 73-81
OPTIMIZATION OF THE THRESHOLD SERVICE SPEED CONTROL IN THE G/M/1 QUEUE
Abstract
Consideration is given to the problem of optimal service speed switching in a G/M/1 queuing system with an objective function which takes into account the fee for customer's service, the penalty for customer's delay in the queue, the penalty for customer's rejection, the penalty for server being idle, and the maintenance costs. The case of finite capacity queue is also considered. The nonlinear optimization problem is formulated and solved in which the objective function is the system's revenue and the control variable is the queue length. The author proves that the objective function is unimodal and formulates the conditions for the existence of an optimal threshold service speed switching and necessary and sufficient conditions for the optimal control.
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[+] About this article
Title
OPTIMIZATION OF THE THRESHOLD SERVICE SPEED CONTROL IN THE G/M/1 QUEUE
Journal
Informatics and Applications
2022, Volume 16, Issue 1, pp 73-81
Cover Date
2022-03-30
DOI
10.14357/19922264220111
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queuing system; threshold control; system costs
Authors
Ya. M. Agalarov 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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